I was planning to have my second set of twins the same way my 1st happened: natural. When they told me my girl was stuck and her heart rate was dropping, AND my BP was rising the said it was time for an emergency C-sect. I'll be honest, I freaked out! I didn't take that so well, and had a lot of complications with mine, (blood loss, slow heal time, local numbness, spinal headache, etc.) So I've heard, my case isn't that common, either. Most women walk and function normally within the week.
I wrote this not to panic you, but to make you aware that as with ANY surgical procedure, no matter how small, there are risks involved. If you trust your doctor and know they have your best interests in mind, as well as your child's, then by all means proceed. If not, find another doc you do trust and see what or who they recommend.
It happened to me that my first doc was not interested in complete care of me, nor the babies I carried, so I went to one I did trust. Even after he told me about the emergency c-section, I became ok with the idea because I felt his willingness to help. He was there through the whole process and, as strenuous as it was I felt some sense of security. Through him, I also found a string of other great docs.
A c-section is a scary idea, I know, but it doesn't have to be if you trust who you put in charge of your care. They will suggest all the things in the world, but ultimately you have say over who, what, and how things happen in the delivery room :)
Good luck and congratulations!
C.C.